{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:25Z","timestamp":1760143645408,"version":"build-2065373602"},"reference-count":70,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T00:00:00Z","timestamp":1708473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Labex OSE","award":["ANR\u201310\u2013LABX\u201393\u201301","AID\u20132020\u201365\u20130057"],"award-info":[{"award-number":["ANR\u201310\u2013LABX\u201393\u201301","AID\u20132020\u201365\u20130057"]}]},{"name":"FireBall project","award":["ANR\u201310\u2013LABX\u201393\u201301","AID\u20132020\u201365\u20130057"],"award-info":[{"award-number":["ANR\u201310\u2013LABX\u201393\u201301","AID\u20132020\u201365\u20130057"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>Two groups produce a network good perceived by a third party, such as a police or military institution, as a \u2018public bad\u2019, referred to as \u2018crime\u2019 for simplicity. These two groups, considered mafias, are assumed to be antagonists, whether they are enemies or competitors in the same market, causing harm to each other\u2019s activities. This paper provides guidelines for the policymaker, typically the police, seeking to minimize overall crime levels by internalizing these negative externalities. One specific question is investigated: the allocation of resources for the police. In general, we recommend a balanced crackdown on both antagonists, but an imbalance in group sizes may lead the police to focus on the more criminal group.<\/jats:p>","DOI":"10.3390\/g15020006","type":"journal-article","created":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T06:50:22Z","timestamp":1708498222000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Model of Competing Gangs in Networks"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4997-4071","authenticated-orcid":false,"given":"Alexis","family":"Poindron","sequence":"first","affiliation":[{"name":"Unit\u00e9 d\u2019\u00c9conomie Appliqu\u00e9e, ENSTA Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nizar","family":"Allouch","sequence":"additional","affiliation":[{"name":"School of Economics, University of Kent, Canterbury CT2 7NZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1111\/j.1468-0262.2006.00709.x","article-title":"Who\u2019s who in networks. Wanted: The key player","volume":"74","author":"Ballester","year":"2006","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1111\/j.0020-6598.2004.00292.x","article-title":"Social networks and crime decisions: The role of social structure in facilitating delinquent behavior","volume":"45","author":"Zenou","year":"2004","journal-title":"Int. Econ. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cao, Z., Gao, H., Qu, X., Yang, M., and Yang, X. (2013). Fashion, cooperation, and social interactions. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0049441"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1111\/j.1467-937X.2009.00550.x","article-title":"Peer Effects and Social Networks in Education","volume":"76","author":"Patacchini","year":"2009","journal-title":"Rev. Econ. Stud."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1162\/jeea.2010.8.1.34","article-title":"Deliquent networks","volume":"8","author":"Ballester","year":"2010","journal-title":"J. Eur. Econ. Assoc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"104969","DOI":"10.1016\/j.jet.2019.104969","article-title":"Social norms in networks","volume":"185","author":"Ushchev","year":"2020","journal-title":"J. Econ. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1307\/mmj\/1028989917","article-title":"On the notion of balance of a signed graph","volume":"2","author":"Harary","year":"1953","journal-title":"Mich. Math. J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Temurshoev, U. (2008). Who\u2019s Who in Networks. Wanted: The Key Group, NET Institute. Working Papers 08-08.","DOI":"10.2139\/ssrn.1285752"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1111\/iere.12275","article-title":"Rumors and Social Networks","volume":"59","author":"Bloch","year":"2018","journal-title":"Int. Econ. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Galam, S. (2012). Sociophysics: A Physicist\u2019s Modeling of Psycho-Political Phenomena, Springer.","DOI":"10.1007\/978-1-4614-2032-3"},{"key":"ref_11","first-page":"011105","article-title":"Phase transitions in the q-voter model with two types of stochastic driving","volume":"86","author":"Nyczka","year":"2012","journal-title":"Phys. Rev."},{"key":"ref_12","unstructured":"Berenbrink, P., Giakkoupis, G., Kermarrec, A., and Mallmann-Trenn, F. (2016). Bounds on the Voter Model in Dynamic Networks. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.geb.2019.08.009","article-title":"The swing voter\u2019s curse in social networks","volume":"118","author":"Buechel","year":"2019","journal-title":"Games Econ. Behav."},{"key":"ref_14","unstructured":"Rogers, E.M. (2003). Diffusion of Innovations, Simon and Schuster. [5th ed.]."},{"key":"ref_15","unstructured":"Rodriguez, M., and Sch\u00f6lkopf, B. (July, January 26). Influence maximization in continuous time diffusion networks. Proceedings of the 29th International Conference on Machine Learning, ICML 2012, Edinburgh, UK."},{"key":"ref_16","unstructured":"Banerjee, A., Chandrasekhar, A., Duflo, E., and Jackson, M.O. (2023, November 01). Available online: https:\/\/economics.mit.edu\/sites\/default\/files\/publications\/Gossip-%20Identifying%20Central%20Individuals%20in%20a%20Socia.pdf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1080\/01621459.1974.10480137","article-title":"Reaching a consensus","volume":"69","author":"DeGroot","year":"1974","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1080\/0022250X.1990.9990069","article-title":"Social influences and opinion","volume":"15","author":"Friedkin","year":"1990","journal-title":"J. Math. Sociol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1142\/S0129183100000936","article-title":"Opinion evolution in closed community","volume":"11","author":"Sznajd","year":"2001","journal-title":"Int. J. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1162\/00335530360698469","article-title":"Persuasion bias, social influence, and unidimensional opinions","volume":"118","author":"DeMarzo","year":"2003","journal-title":"Q. J. Econ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.physa.2007.03.034","article-title":"The role of inflexible minorities in the breaking of democratic opinion dynamics","volume":"381","author":"Galam","year":"2007","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1287\/opre.2015.1448","article-title":"The Evolution of Beliefs over Signed Social Networks","volume":"64","author":"Shi","year":"2013","journal-title":"Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.jedc.2014.12.006","article-title":"Opinion dynamics and wisdom under conformity","volume":"52","author":"Buechel","year":"2015","journal-title":"J. Econ. Dyn. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1162\/jeea.2010.8.1.90","article-title":"Keeping up with the neighbors: Social interaction in a market economy","volume":"8","author":"Ghiglino","year":"2010","journal-title":"J. Eur. Econ. Assoc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1017\/nws.2012.7","article-title":"Diffusion and contagion in networks with heterogeneous agents and homophily","volume":"1","author":"Jackson","year":"2013","journal-title":"Netw. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1257\/mic.2.1.112","article-title":"Naive learning in social networks and the wisdom of crowds","volume":"2","author":"Golub","year":"2010","journal-title":"Am. Econ. J. Microecon."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.econlet.2018.02.019","article-title":"The transmission of continuous cultural traits in endogenous social networks","volume":"167","author":"Hellmann","year":"2018","journal-title":"Econ. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S1286-4579(02)00058-8","article-title":"Sexual networks: Implications for the transmission of sexually transmitted infections","volume":"5","author":"Liljeros","year":"2003","journal-title":"Microbes Infect."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1177\/1043463108096787","article-title":"Social influence, binary decisions and collective dynamics","volume":"20","author":"Watts","year":"2008","journal-title":"Ration. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"797","DOI":"10.2307\/2118364","article-title":"A simple model of herd behavior","volume":"107","author":"Banerjee","year":"1992","journal-title":"Q. J. Econ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.2307\/2951507","article-title":"Information revelation and strategic delay in a model of investment","volume":"62","author":"Chamley","year":"1994","journal-title":"Econometrica"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chamley, C.P. (2004). Rational Herds: Economic Models of Social Learning, Cambridge University Press.","DOI":"10.1017\/CBO9780511616372"},{"key":"ref_33","unstructured":"Girard, R. (1966). Deceit, Desire and the Novel: Self and Other in Literary Structure, Johns Hopkins University."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Girard, R. (1977). Violence and the Sacred, Johns Hopkins University.","DOI":"10.56021\/9780801819636"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Girard, R. (1986). The Scapegoat, The Johns Hopkins University Press.","DOI":"10.1353\/book.98235"},{"key":"ref_36","unstructured":"Girard, R. (1987). Things Hidden Since the Foundation of the World, Stanford University Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/TAC.2012.2224251","article-title":"Consensus Problems on Networks With Antagonistic Interactions","volume":"58","author":"Altafini","year":"2013","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_38","first-page":"4379","article-title":"The hipster effect: When anticonformists all look the same","volume":"24","author":"Touboul","year":"2019","journal-title":"Discret. Contin. Dyn. Syst.-B"},{"key":"ref_39","unstructured":"Mahfuze, A. (2023, November 01). Product Quality and Social Influence. Available online: https:\/\/papers.ssrn.com\/sol3\/Delivery.cfm\/SSRN_ID3853128_code2765587.pdf?abstractid=3853128&mirid=1."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s001820400178","article-title":"Network formation and anti-coordination games","volume":"33","author":"Goyal","year":"2004","journal-title":"Int. J. Game Theory"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.geb.2005.12.006","article-title":"Anti-coordination and social interactions","volume":"58","year":"2007","journal-title":"Games Econ. Behav."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1142\/S0219198909002145","article-title":"Network formation, cost sharing and anti-coordination","volume":"11","year":"2009","journal-title":"Int. Game Theory Rev."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Altafini, C. (2012). Dynamics of Opinion Forming in Structurally Balanced Social Networks. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0038135"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.mathsocsci.2013.07.003","article-title":"A model of influence based on aggregation functions","volume":"66","author":"Grabisch","year":"2013","journal-title":"Math. Soc. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1524","DOI":"10.1109\/TAC.2015.2471655","article-title":"Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization","volume":"61","author":"Proskurnikov","year":"2016","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1086\/226707","article-title":"Threshold models of collective behavior","volume":"83","author":"Granovetter","year":"1978","journal-title":"Am. J. Sociol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"5766","DOI":"10.1073\/pnas.082090499","article-title":"A simple model of global cascades on random networks","volume":"99","author":"Watts","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.jet.2006.06.006","article-title":"Public goods in networks","volume":"135","author":"Kranton","year":"2007","journal-title":"J. Econ. Theory"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1257\/aer.104.3.898","article-title":"Strategic interaction and networks","volume":"104","author":"Kranton","year":"2014","journal-title":"Am. Econ. Rev."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1080\/0022250X.2013.803100","article-title":"Key player policies when contextual effects matter","volume":"38","author":"Ballester","year":"2014","journal-title":"J. Math. Sociol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1111\/jpet.12298","article-title":"Public goods and public bads","volume":"10","author":"Buchholz","year":"2018","journal-title":"J. Public Econ. Thory"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.geb.2010.10.010","article-title":"Social Interactions and Spillovers","volume":"72","author":"Cabrales","year":"2011","journal-title":"Games Econ. Behav."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1080\/0022250X.1986.9990008","article-title":"A formal theory of social power","volume":"12","author":"Friedkin","year":"2010","journal-title":"J. Math. Sociol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1080\/00222500701542467","article-title":"On Some Properties of the Hoede-Bakker Index","volume":"31","author":"Rusinowska","year":"2007","journal-title":"J. Math. Sociol."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Braham, M., and Steffen, F. (2008). Power, Freedom, and Voting, Springer.","DOI":"10.1007\/978-3-540-73382-9"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/moor.1120.0570","article-title":"Opinion Fluctuations and Disagreement in Social Network","volume":"38","author":"Acemoglu","year":"2010","journal-title":"Math. Oper. Res."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1086\/228631","article-title":"Power and centrality: A family of measures","volume":"92","author":"Bonacich","year":"1987","journal-title":"Am. J. Sociol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"036104","DOI":"10.1103\/PhysRevE.78.036104","article-title":"Mobility and Social Network Effects on Extremist Opinions","volume":"78","author":"Martins","year":"2008","journal-title":"Phys. Rev. Stat. Nonlinear Soft Matter Phys."},{"key":"ref_59","first-page":"413","article-title":"Centrality Measures in Networks","volume":"61","author":"Bloch","year":"2016","journal-title":"SSRN Electron. J."},{"key":"ref_60","unstructured":"Allouch, N., Meca, A., and Polotskaya, K. (2023, November 01). The Bonacich Shapley Centrality. Available online: https:\/\/www.kent.ac.uk\/economics\/repec\/2106.pdf."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Jackson, M.O. (2008). Social and Economic Networks, Princeton University Press.","DOI":"10.1515\/9781400833993"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Bramoull\u00e9, Y., Galeotti, A., and Rogers, B. (2016). The Oxford Handbook of the Economics of Networks, Oxford University Press.","DOI":"10.1093\/oxfordhb\/9780199948277.001.0001"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/j.jet.2015.01.007","article-title":"On the private provision of public goods on networks","volume":"157","author":"Allouch","year":"2015","journal-title":"J. Econ. Theory"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s11127-007-9268-4","article-title":"The roles of foreign aid and education in the war on terror","volume":"135","author":"Azam","year":"2008","journal-title":"Public Choice"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s11127-011-9798-7","article-title":"Why suicide-terrorists get educated, and what to do about It","volume":"153","author":"Azam","year":"2012","journal-title":"Public Choice"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1093\/oep\/50.4.563","article-title":"On economic causes of civil war","volume":"50","author":"Collier","year":"1998","journal-title":"Oxf. Econ. Pap."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.geb.2018.11.012","article-title":"A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis","volume":"114","author":"Parise","year":"2020","journal-title":"Games Econ. Behav."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (2012). Matrix Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9781139020411"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1137\/1031049","article-title":"Updating the inverse of a matrix","volume":"31","author":"Hager","year":"1989","journal-title":"SIAM Rev."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/BF01456804","article-title":"Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung","volume":"71","author":"Weyl","year":"1912","journal-title":"Math. Ann."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/2\/6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:25Z","timestamp":1760104945000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/2\/6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,21]]},"references-count":70,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["g15020006"],"URL":"https:\/\/doi.org\/10.3390\/g15020006","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2024,2,21]]}}}